Vertical throw flight time calculator
A ball thrown straight up at 24.5 m/s under 9.80665 m/s² gravity stays in the air for 4.996609443592 s before passing its launch height again. Enter launch speed and gravity to get the flight time. Free in your browser.
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Worked example
- Initial velocity
- 24.5
- Gravity
- 9.80665
- Flight time
- 4.9966094436
The vertical throw flight time calculator finds how long an object remains in the air when it is launched straight upward and returns to exactly the same height.
Understand what total flight time means
For this calculation, flight begins at the instant an object leaves the launch height with an upward velocity and ends when it crosses that same height on the way down. The result therefore includes two equal parts under the ideal model: time spent rising until vertical velocity reaches zero, and time spent falling back through the original level. The calculator expects initial velocity and gravity to use compatible units.
For example, meters per second paired with meters per second squared produces seconds. Feet per second paired with feet per second squared also produces seconds. The returned gravity is treated as a magnitude, so a negative sign convention is normalized rather than allowed to make a negative duration.
A zero launch velocity gives zero flight time because the object has no upward motion. Gravity, however, cannot be zero because division by zero provides no finite return time in this model.
Use the formula with the right assumptions
The equation describes ideal one-dimensional motion under constant gravitational acceleration. It assumes the object is thrown perfectly vertically, starts and finishes at the same elevation, and experiences no aerodynamic drag, lift, propulsion, collision, or change in gravity during the trip. Those assumptions make the upward and downward durations symmetric.
Real objects can behave differently: a ball with substantial drag usually descends differently from the way it rises, wind can introduce sideways movement, and a landing point above or below the launch point breaks the equal-time symmetry. The initial velocity should be the upward component at release, not an average speed and not the speed observed later in the trajectory. Gravity should be the local acceleration magnitude expressed in units consistent with velocity.
Standard Earth gravity is often approximated near 9.81 m/s², but a classroom problem may specify another value. Use that stated value instead of silently substituting a default, because flight time changes inversely with gravity.
What you can do with it
Check a kinematics exercise
Verify the complete up-and-down duration from a stated vertical launch velocity and gravitational acceleration.
Plan a classroom demonstration
Estimate when a vertically launched object should return to its release height under the ideal model.
Validate simulation output
Compare a constant-gravity simulation against a deterministic analytic flight-time reference.
FAQ
What does the result represent?
It is the total time from an upward launch until the object returns to the same height, including ascent and descent.
Does the calculator include air resistance?
No. It uses ideal vertical motion with constant gravity and no drag, lift, wind, or propulsion.
Which units can I use?
Use any consistent velocity and acceleration units. Meters per second with meters per second squared, or feet per second with feet per second squared, produces time in seconds.
How long does a ball thrown up at 24.5 m/s stay in the air?
It stays up for 4.996609443592 s with standard gravity of 9.80665 m/s², until it returns to the launch height. The time is twice the launch speed divided by gravity.
What happens if the launch speed or gravity is zero?
A zero launch speed gives a flight time of zero, since the object never rises. Gravity cannot be zero, because there would be no return, and a negative sign is treated as its magnitude.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/mech/vertical-throw-flight-time \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"initial_velocity":20,"gravity":9.80665}'const res = await fetch("https://api.kit.forhosting.com/mech/vertical-throw-flight-time", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"initial_velocity": 20,
"gravity": 9.80665
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/vertical-throw-flight-time",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"initial_velocity": 20,
"gravity": 9.80665
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/vertical-throw-flight-time", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"initial_velocity":20,"gravity":9.80665}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"initial_velocity":20,"gravity":9.80665}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/vertical-throw-flight-time", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"initial_velocity": 20,
"gravity": 9.80665
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.vertical_throw_flight_time",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Enter the upward initial velocity and gravitational acceleration, and the calculator applies the ideal constant-gravity relation T = 2v/g. It reports the complete trip, including both the rise and the fall. This focused result is useful for physics exercises, quick engineering estimates, classroom demonstrations, and automated checks where air resistance can be ignored.
Understand what total flight time means
Each part lasts v/g, so adding them gives T = 2v/g.
Interpret and automate the result
Small differences from another answer commonly come from using a rounded gravity value such as 9.8 instead of 9.80665, not from a different method. Keep more precision in the inputs when comparison tolerances are strict, and round only the displayed answer if a course or report requires a particular number of decimal places. Read flight_time as the duration from launch to the return crossing at launch height. The calculation is deterministic: identical inputs always return identical JSON, with no network request, random value, or current-time dependency. That makes it suitable for bulk validation even though each request represents one calculation. The browser version is convenient for individual checks, while API execution costs $0.002 per request when you need to integrate the same calculation into tests, educational tools, experiment logs, or repeatable data-processing workflows.
Technical questions
Why is the formula T = 2v/g?
The ascent lasts v/g under constant gravity. Returning to the same height takes an equal amount of time, so the total is twice that value.
What happens when gravity is zero?
The request returns an invalid_input error because division by zero cannot produce a finite return time.
How much does API execution cost?
Each API request costs $0.002. The calculator can also run free in the browser.